In this paper a three-dimensional non-holonomic integrator (NI) with drift terms is considered. For this type of plant, the question how to obtain desired piecewise constant output functions with minimum norm control inputs is explored. It is shown that this can be achieved by a nonlinear controller that provides simultaneous modulation of both the amplitude and the frequency of the harmonic input vector. The internal states are implicitly forced to follow natural periodic orbits satisfying the nonholonomic constraints of the plant. Global asymptotic stability and high dynamics in the output response are achieved. The problem of singularity at zero initial state is solved by a time optimal control scheme for the internal states. By combining the nonlinear controller and the time-optimal controller using an appropriate switching strategy, a powerful control concept can be established. The torque control of an induction machine is considered as an illustrative example for the application of the control scheme. Experimental results of the closed loop feedback control system are presented. (c) 2012 Elsevier Ltd. All rights reserved.